The radii of the top and bottom circular faces of a bucket in the shape of a frustum of a cone are 35 cm and 28 cm, respectively. Its capacity is 187.88 litres. What is the height of the bucket? (Take π = \(\frac{22}{7}\)

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AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)
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  1. 45 cm
  2. 50 cm
  3. 60 cm
  4. 80 cm

Answer (Detailed Solution Below)

Option 3 : 60 cm
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Detailed Solution

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Given:

R = radius of the top circular face = 35 cm

r = radius of the bottom circular face = 28 cm

h = height of the bucket

Formula used:

Volume of frustum = \(\dfrac{1}{3} \pi h (R^2 + r^2 + Rr)\)

Volume of the frustum = 187.88 litres = 187.88 × 1000 cm3 = 187880 cm3

Calculations:

Volume of the frustum = 187880 cm3

\(\dfrac{1}{3} \pi h (R^2 + r^2 + Rr) = 187880\)

\(\dfrac{1}{3} \times \dfrac{22}{7} \times h \times (35^2 + 28^2 + 35 \times 28) = 187880\)

\(\dfrac{22}{21} \times h \times (1225 + 784 + 980) = 187880\)

\(\dfrac{22}{21} \times h \times 2989 = 187880\)

\(h = \dfrac{187880 \times 21}{22 \times 2989}\)

\(h = \dfrac{3945480}{65758}\)

⇒ h = 60 cm

∴ The correct answer is option 3.

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